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[Witherweaver]

I'm predicting someone will say that example is extremely contrived, and it is.  But pretend you don't know what sin(x) and cos(x) look like.. you don't have a graphing calculator or whatever, you didn't really pay attention when they defined them from triangles, you don't know their values at the "special angles".  So you don't know they should be zero at points.  You're just looking at the problem that says to prove something, and all you know is that sin^2(x)+cos^2(x) = 1.

The false statement here is bundled with a true one.  You assume the entirety and get a true statement (sin x = sin x) and use it to show your original assumption is okay.  That doesn't work.

Maybe someone can think of a more organic example.

[Kirian]

I think part of the problem may be the phrasing of my proof.  Consider without any assumptions:

(1) x = 2 is a solution of Eqn. A iff both sides of Eqn. A will evaluate to the same number when x is set to 2.
(2) Both sides of Eqn. A evaluate to 2 when x = 2. (Demonstrated)
(3) Therefore, x = 2 is a solution of Eqn. A.

I think the problem is I wasn't using the biconditional, and I'm almost certain the biconditional applies to solutions of equations.  Now, it's reasonable to question whether what the student presented satisfies as a demonstration of (2).  And using the wrong reasoning to demonstrate (2) is certainly cause for deduction of points.

[Witherweaver]

I think part of the problem may be the phrasing of my proof.  Consider without any assumptions:

(1) x = 2 is a solution of Eqn. A iff both sides of Eqn. A will evaluate to the same number when x is set to 2.
(2) Both sides of Eqn. A evaluate to 2 when x = 2. (Demonstrated)
(3) Therefore, x = 2 is a solution of Eqn. A.

I think the problem is I wasn't using the biconditional, and I'm almost certain the biconditional applies to solutions of equations.  Now, it's reasonable to question whether what the student presented satisfies as a demonstration of (2).  And using the wrong reasoning to demonstrate (2) is certainly cause for deduction of points.

Yes, but (2) was not correctly demonstrated by the student. Saying "f(x)=g(x), ...., 2=2" does not demonstrate that a and b evaluate to 2 (or whatever) when plugging in x=2.  It only shows that 2=2 when f(x) = g(x). There could have been manipulations that are only true under the assumption that f(x) = g(x), but are false when that assumption does not hold.  The obvious counterexample is when f(x) = -2^{1/2}, g(x) = 2^{1/2}.  Or if you want it to be hidden more come up with functions f, g so that f(2) = -2^{1/2}, g(2) = 2^{1/2} but it's not so obvious..  Then f(x) = g(x) will imply 2=2, but f!=g.

[Watno]

I think the main concern here is what a student writing such a proof means to say.
I think the likely thing ist that the lines were supposed to be a chain of equivalences, in which case that should have been made clear.
If the lines were meant to be a chain of implications,  the whole reasoning would be flawed and it would put the student in danger of making false conclusions as outlined in examples where implications that aren't equivalences were used, which would be a huge problem.

Btw, my preferred way to denote verification of identities is going like this:

Code: [Select]

T1     S1
=      =
T2     S2
=      =
...   ...
=      =
Tn  =  Sn


[AHoppy]

...

+1 for the Billy Joel reference

[pingpongsam]

[Polk5440]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

I taught undergrad courses while I was doing my PhD, but I went into industry instead of academia.

I have taught undergrad Econ.

I have tutored high school through MBA math and Econ at various points in time as well, but I understand that's not the same .

[Axxle]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

[sudgy]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

Vote: Axxle

[AndrewisFTTW]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

Vote: Axxle

If Axxle is a substitute teacher I'm looking at you next.

vote: Axxle

[sudgy]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

Vote: Axxle

If Axxle is a substitute teacher I'm looking at you next.

vote: Axxle

I'm just a student!  Axxle claimed third party, that's usually bad for the students.

[pingpongsam]

[SirPeebles]

Are you playing Axxle and Allies?

[Watno]

The Axxle of Evil?

[Axxle]

All my tshirts are of size Axxle.

[Tables]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

Vote: Axxle

If Axxle is a substitute teacher I'm looking at you next.

vote: Axxle

Oh gosh as of tomorrow, I'm a substitute teacher (no really, this is actually true IRL), but please don't vote me!

[Kirian]

Also:  How many college instructors do we have in this thread, anyway?  I count at least three specifically declared (me, Peebles, shraeye).  Anyone else?

Claim: third party, neither professor nor student

Vote: Axxle

If Axxle is a substitute teacher I'm looking at you next.

vote: Axxle

Oh gosh as of tomorrow, I'm a substitute teacher (no really, this is actually true IRL), but please don't vote me!

A sub?  Dude, you're so screwed...

...or maybe kids in Britain aren't as troublesome as kids in the US?

[Kirian]

Everything I know about British schools comes from Harry Potter (for secondary school) and Connie Willis's Fire Watch universe (for colleges).

[AndrewisFTTW]

Everything I know about British schools comes from Harry Potter (for secondary school) and Connie Willis's Fire Watch universe (for colleges).

It's all true.

[eHalcyon]

I don't watch baseball.  Can someone explain what's happening here?

The post had this additional context:

"This double play was officially scored: 4-3-3-6-3-4-3-4-5-2."

[Kirian]

I don't watch baseball.  Can someone explain what's happening here?

The post had this additional context:

"This double play was officially scored: 4-3-3-6-3-4-3-4-5-2."

I can't tell from the gif exactly what's up, but the number notation at the bottom indicates who had the ball during the play, with 3 = 1st base, 4 = 2nd base, 5 = shortstop, 6 = 3rd base, and 2 = catcher.

I don't watch baseball either, but I'd love to see the video so I can tell what's going on.

[AndrewisFTTW]

I  can't tell exactly from the meme but there are two rundowns and I think the guy going for home is tagged out while the guy who was won first gets to to third. Maybe there were runners on first and second, somebody flied out and the runners tagged? There's probably a full video somewhere.

[Kirian]

My bad, SS is 6, with 3-4-5 for 1st, 2nd, 3rd bases.

I  can't tell exactly from the meme but there are two rundowns and I think the guy going for home is tagged out while the guy who was won first gets to to third. Maybe there were runners on first and second, somebody flied out and the runners tagged? There's probably a full video somewhere.

After doing a search it appears there were runners on first and second, the batter hit to second, second throws to first and tags the base to put the batter out (4-3).  Meanwhile, the runner on first has taken off for second; because the ball touched the ground, he didn't have to tag back to first.  So the first baseman throws to the shortstop near second (3-6) forcing the runner toward first, causing a back-and-forth between the first and second basemen (6-3-4-3-4).

And all of that was the runner on first distracting everyone from the runner on second making his way home, but the seocnd baseman realized what's up, throws to third base, who throws to the catcher, who tags out that runner (4-5-2).

[ashersky]

I don't watch baseball.  Can someone explain what's happening here?

The post had this additional context:

"This double play was officially scored: 4-3-3-6-3-4-3-4-5-2."

I can't tell from the gif exactly what's up, but the number notation at the bottom indicates who had the ball during the play, with 3 = 1st base, 4 = 2nd base, 5 = shortstop, 6 = 3rd base, and 2 = catcher.

I don't watch baseball either, but I'd love to see the video so I can tell what's going on.

Actually, you switched 3rd base (5) and shortstop (6), but otherwise correct.

The first out of the double play was the batter being thrown out at first base after grounding it to the second baseman.  By getting the out at first base, there was no longer any force outs at subsequent bases.  From what I can tell, there were runners on first and second when the batter grounded out.  After the first baseman received the ball from the second baseman (4-3), they attempted to get the runner going from first to second out.  They caught him in a rundown that had the first baseman throwing the shortstop (covering second), then back to the first baseman, then on to the second baseman, then back to the first baseman again, and again to the second baseman (3-6-3-4-3-4).  At this point, the runner who was originally on second base had taken a big turn around third base thinking about trying to score, so the second baseman turned and fired the ball to third base in an attempt to get him out there (4-5).  The runner broke for home, chased by the third baseman, who tossed it to the catcher who applied to tag for the second out of the double play (5-2).

I think the scoring is incorrect.  It should have been a 4-3-6-3-4-3-4-5-2 double play (there's an extra 3 in the caption - you only put one number per touch of the ball, even if it was 4-3 and then 3-6; it would just be 4-3-6).

[AndrewisFTTW]

Yeah. That.